## Linear Operators: Spectral theory |

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If the domain D ( T ) of the operator T is

If the domain D ( T ) of the operator T is

**dense**in H then the domain D ( T * ) consists , by definition , of all y in v for which ( Tx , y ) is continuous for x in D ( T ) . Since D ( T ) is**dense**in y there is ( IV.4.5 ) a uniquely ...Page 1271

Let T be a symmetric operator with domain D ( T )

Let T be a symmetric operator with domain D ( T )

**dense**in H. Then if x is in D ( T ) , we have | ( T + il ) x12 = ( Tx , Tx ) F 1 ( x , Tx ) + i ( Tx , x ) + ( x , x ) = Tx2 + \ x22x12 . This shows that if ( T + il ) x = 0 , then x = 0 ...Page 1905

... rules of , ( 2 )

... rules of , ( 2 )

**Dense**convex sets , V.7.27 ( 437 )**Dense**linear manifolds , V.7.40–41 ( 438–439 )**Dense**set ... III.3.8 ( 125 ) nowhere**dense**set , 1.6.11 ( 21 ) Density of the natural embedding of a B - space X into X ** in the X ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero